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Math Help - disjoint intervals

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    disjoint intervals

    Let F be a collection of disjoint intervals of real numbers. This means that if I and J are two distinct intervals in F, then the intersection of I and J is zero. Prove that the set F is countable.
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    Quote Originally Posted by friday616 View Post
    Let F be a collection of disjoint intervals of real numbers. This means that if I and J are two distinct intervals in F, then the intersection of I and J is empty?. Prove that the set F is countable.
    Between any two real numbers there is a rational number.
    Properly defined a closed interval looks like \left[ {a,b} \right] = \left\{ {x:a < b\;\& \;a \leqslant x \leqslant b} \right\}.
    Thus in each closed interval in the collection \mathcal{F} there is a rational number.
    Because the set of rationals is countable the collection \mathcal{F} is countable.
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    Quote Originally Posted by friday616 View Post
    Let F be a collection of disjoint intervals of real numbers. This means that if I and J are two distinct intervals in F, then the intersection of I and J is zero. Prove that the set F is countable.
    Do you consider single point sets, such as [1,1] to be intervals?
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